Divide by a Two-Digit Divisor

Transcription

1 CHAPTER 4 connected.mcgraw-hill.com Investigate Animations Vocabulary Divide by a Two-Digit Divisor The BIG Idea How can I divide by two-digit divisors accurately? Math Songs Multilingual eglossary Learn Personal Tutor Virtual Manipulatives Audio Foldables Make this Foldable to help you organize information about division. Estimate Quotients with Two-Digit Divisiors Adjust Quotients Divide by a Two-Digit Divisor Divide Greater Numbers Practice Self-Check Practice egames Worksheets Assessment Review Vocabulary dividend dividendo a number that is being divided is the dividend. Review Vocabulary English Español divisor divisor quotient cociente 158

2 When Will I Use This? Your Turn! You will solve this problem in the chapter. Divide by a Two-Digit Divisor 159

3 Are You Ready for the Chapter? You have two options for checking Prerequisite Skills for this chapter. Text Option Take the Quick Check below. Estimate each product. Tell whether the estimate is greater than or less than the actual product. 1. $ Raul purchases 13 packs of straws for his restaurant from Company A. About how many straws does he have in all? Number of Straws Company per Pack A 225 B 310 Multiply , A musical was sold out for three straight shows. If 825 tickets were sold at each performance, how many tickets were sold in all? Multiply The teacher purchased 13 packs of crayons. There are 24 crayons in each pack. How many crayons are there in all? Online Option Take the Online Readiness Quiz. 160 Divide by a Two-Digit Divisor

4 Multi-Part Lesson 1 Divide by a Two-Digit Divisor PART A B C D Main Idea I will estimate quotients with twodigit divisors. Get ConnectED GLE Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution. GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. Also addresses GLE Estimate Quotients with Two-Digit Divisors You can use rounding and compatible numbers to estimate quotients when dividing by two-digit divisors. By estimating first, you can determine the reasonableness of your results. FLIERS The school principal has 812 fliers to pass out equally to 19 different teachers. About how many fliers will each teacher receive? Estimate Step 1 Round the divisor to the nearest ten and round the dividend to the nearest hundred Step 2 Divide mentally = 40 So, each teacher would receive about 40 fliers. CAMPING Camp Hickory has 425 campers. If there are 64 counselors, about how many campers will be assigned to each counselor? Estimate Step 1 Round the divisor to the nearest ten. Step 2 Change the dividend to 420 because 42 and 6 are compatible numbers Step 3 Divide mentally = 7 So, about 7 campers will be assigned to each counselor. Lesson 1A Divide by a Two-Digit Divisor 161

5 Another way to write is Use Rounding and Compatible Numbers Estimate Step 1 Round the divisor to the nearest ten. Step 2 Change the dividend to a number that is compatible with 40. Notice it is easy to divide 240 by 40. Step 3 Divide mentally. So, is about 6. Check 6 40 = 240 and = 6 Estimate. Show your work. See Examples A classroom of 28 students used 612 pencils over the school year. If each student used the same number of pencils, about how many pencils did each student use? 10. A box of cereal contains 340 grams. If there are 12 servings, about how many grams are there in one serving? Show how you estimated. Explain why your answer is reasonable. 11. There are 598 goldfish divided equally among 23 fish tanks. About how many goldfish are in each tank? 12. Suppose the number of goldfish in Exercise 11 increased to 605, would your estimate change? Explain. 13. E TALK MATH Is it possible to have more than one estimate for a division problem? Explain. Give an example. 162 Divide by a Two-Digit Divisor

6 Estimate. t Show your work. See Examples 1 3 PRACTICE EXTRA Begins on page EP Sudi has collected 643 stamps and wants to place them all in an album. Each page of the album holds 82 stamps. He estimates that he needs 80 pages. How can you tell his estimate is wrong? 23. A school bus holds 42 people. Suppose 381 students ride the bus to school. About how many buses are needed? Explain why your estimate is reasonable. Use the information to solve the problem. A Big Book 24. Estimate the number of pages Antwan needs to read each day. 25. REASONING Explain how you can use mental math to estimate WHICH ONE DOESN T BELONG? Which of these equations is NOT a reasonable estimate for ? = = = = E WRITE MATH Explain when it would be useful to estimate. Lesson 1A Divide by a Two-Digit Divisor 163

7 Multi-Part Lesson 1 PART Divide by a Two-Digit Divisor A B C D Main Idea I will explore dividing by two-digit divisors using models. Materials base-ten blocks Divide by a Two-Digit Divisor Gary is saving up to buy a guitar that costs $180. Suppose he saves for 12 months. How much money does he need to save each month? Find Use base-ten blocks to find the quotient. Step 1 Model 180 using base-ten blocks. Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. Also addresses GLE Step 2 Regroup the hundred block into tens. Divide the tens equally into 12 groups. There are 18 tens. There are still 6 tens that need to be divided. 164 Divide by a Two-Digit Divisor

8 Step 3 Regroup the remaining tens as ones. Divide the ones equally into 12 groups. There are 60 ones. Each group contains 1 ten and 5 ones or 15. So, each month Gary needs to save $15. Check Use multiplication to check your answer. $15 12 = $180 About It 1. In the Explore Activity you started by placing 1 ten in each group. What does that show about the place value of the first digit of the quotient? 2. What would happen if the cost of the guitar was $192? Would the amount to save each month increase or decrease? Explain. 3. Suppose Jamie chose to save for 13 months instead of 12 months. Will the amount he needs to save per month increase or decrease? Explain your answer. and Apply It Use models to find each quotient E TALK MATH How can you use multiplication to check your answers for Exercises 4 9? Lesson 1B Divide by a Two-Digit Divisor 165

9 Multi-Part Lesson 1 PART Divide by a Two-Digit Divisor A Main Idea I will divide up to a three-digit number by a two-digit divisor. Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers and decimals. SPI Solve problems involving the division of twoand three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE B C D E Divide by a Two-Digit Divisor In this lesson, you will learn how to divide by a two-digit divisor. Use estimation to help place the first digit in the quotient. FOOD A full sheet cake serves 76 people. How many sheet cakes are needed to serve 836 people? Check your answer for reasonableness. Find Estimate = 10. So, the first digit is in the tens place. Step 1 Write as Step 2 Divide the tens Divide: Multiply: Subtract: Compare: 7 < 76 Step Divide the ones. Bring down the ones. Divide: Multiply: 1 76 Subtract: Compare: 0 < 76 Check for Reasonableness Compare to the estimate, 10. Since 11 is close to 10, the answer is reasonable. So, 11 cakes are needed to serve 836 people. As with division by a one-digit divisor, it is possible to have a remainder when you divide by a two-digit divisor. 166 Divide by a Two-Digit Divisor

10 Division with a Remainder Find You can check division with a remainder. Multiply the quotient and the divisor. Then add the remainder Estimate = 25 Step 1 Write as Step 2 Divide the tens < 30 Step 3 Divide the ones. 25 R Bring down the ones < 30 Check for Reasonableness Compare to the estimate, 25. Since 25 R1 is close to 25, the answer is reasonable. So, is 25 R1. MEASUREMENT Mackenzie volunteered 204 hours last year. If she volunteered the same number of hours each month, how many hours did she volunteer each month? Find Estimate = 20 Step 1 Write as Step 2 Divide the tens < 12 Step 3 Divide the ones Bring down the ones Check for Reasonableness Compare to the estimate, 20. Since 17 is close to 20, the answer is reasonable. So, Mackenzie volunteered an average of 17 hours each month. Lesson 1C Divide by a Two-Digit Divisor 167

11 Divide. See Examples Mr. Calzada buys flags for his store. Each flag costs $28. How many flags can he buy for $350? E 6. TALK MATH Explain how estimation is used to help you place the first digit in the quotient. Divide. id See Examples 1 3 PRACTICE EXTRA Begins on page EP A boat travels 384 miles in 24 hours. What is the average distance the boat travels in 1 hour? 17. In 31 days Gwen sleeps 248 hours. If she sleeps the same number of hours each night, how many hours does she sleep per night? 16. Dreanne has 288 pictures. Her album holds 12 pictures on each page. How many pages does she need? 18. How many payments of $46 does Will need to make for a bed that costs $644? Use the information to solve the problem. A Big Book 19. How many pages does Antwan need to read each day to finish his 294-page book in 3 weeks? 168 Divide by a Two-Digit Divisor

12 20. OPEN ENDED Write a real-world division problem that has a two-digit quotient that is greater than 40 but less than NUMBER SENSE Without calculating, predict whether will have a 1 or a 2 in the first digit of the quotient. Explain. 22. CHALLENGE Find the quotient of 1,686, E WRITE MATH What are two different ways to check the reasonableness of your quotient? Test Practice 24. A hotel has 21 floors and a total of 861 rooms. Suppose there are the same number of rooms on each floor. Which expression would describe how many rooms are on the 21 st floor? A B C D The principal is placing trophies onto 12 shelves. Suppose an equal number of trophies need to be placed on each shelf. How many trophies can be placed on the first shelf? F. 12 G. 6 H. 5 I. 4 Trophies Type Amount Academic 25 Sports GRIDDED RESPONSE Jalisa s teacher assigned a 364-page book for her to read. Jalisa has 14 days to read the book. If she reads the same number of pages each day, how many pages will she need to read each day to finish the assignment on time? 27. A group of friends equally split the dinner bill shown. If each person paid $16, how many friends paid? A. 7 friends B. 12 friends C. 14 friends Chicken Tacos...$82 Drinks...$28 Salads...$52 Desserts...$33 Tip...$29 Total...$224 D. 16 friends Lesson 1C Divide by a Two-Digit Divisor 169

13 Multi-Part Lesson 1 Divide by a Two-Digit Divisor PART A B C D Problem-Solving Strategy: Solve a Simpler Problem Main Idea I will solve problems by solving a simpler problem. To serve 240 people, you would need to buy 20 cakes from Bryan s Bakery. Each cake serves the same number of people. How many people could you serve if you bought 25 cakes? Understand What facts do you know? 20 cakes can serve 240 people. Plan What do you need to find? How many people can be served by 25 cakes? You can solve the problem by solving a simpler problem. Solve Step 1 Find how many people are served by 1 cake = 12 Each cake serves 12 people. Step 2 Find how many people can be served by 25 cakes. 25 cakes 12 1 cake = 300 So, 25 cakes will serve 300 people. Check Since = 12, and 12 is the amount of people served by one cake, the answer is correct. GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution. 170 Divide by a Two-Digit Divisor

14 Refer to the problem on the previous page. 1. Explain why you first found how many people just 1 cake would serve. 2. How many people could be served by 8 cakes? 3. Look back at Exercise 2. Check your answer. How do you know it is reasonable? Explain. 4. Explain when you would use the solve a simpler problem strategy to solve a problem. PRACTICE EXTRA Begins on page EP2. Solve. Use the solve a simpler problem strategy. 5. Algebra Working separately, 3 teenagers can mow 3 lawns in 3 hours. At this rate, how many lawns can 6 teenagers mow in 9 hours? 6. Measurement Darby is cutting ribbons for balloons. Each ribbon needs to be 3 feet long. How long will it take Darby to make the cuts if each cut takes 3 seconds? 9. Josh watches 720 television shows in one year. If he watches the same number of shows each month, how many shows does he watch in 5 months? 10. Charity and her friend each want to buy a piece of pizza, a drink, and an ice cream cone. Charity has $10 to pay for her and her friend s meal. Does she have enough money? Explain. 7. Find the sum of the whole numbers from 1 through 10. Use this sum to help you find the sum of the whole numbers from 1 through 20. Pizza Drink Ice cream cone $3.00 $1.00 $ Kodi wants to buy a new tennis racket. So far, she has saved $25 plus $7 from each of her two babysitting jobs. How much more money does she need to buy the tennis racket shown below? 11. Algebra At the beach, 4 children working separately made 8 sandcastles in an hour. At this rate, how many sandcastles can 12 children make in a 1 _ 2 hour? $ E WRITE MATH Write a real-world problem that can be solved using the solve a simpler problem strategy. Trade with a partner and solve. Lesson 1D Divide by a Two-Digit Divisor 171

15 Mid-Chapter Check Estimate. Show your work. (Lesson 1A) MULTIPLE CHOICE There were 815 ants in 11 ant farms. If the same number of ants were in each ant farm, about how many ants were in one farm? (Lesson 1A) A. 50 B. 80 C. 100 D The Mitchell family is making payments on the refrigerator shown. If they pay $41 every month, how many months will it take to pay for the refrigerator? (Lesson 1C) 16. MULTIPLE CHOICE A package of construction paper holds 525 pieces of paper with 15 different colors. If there are the same number of pieces of paper per color, how many pieces of paper of each color are there? (Lesson 1C) 525 sheets F. 35 H. 75 G. 50 I Addison has 512 beads to make 16 necklaces. How many beads can she put on each necklace, if each necklace gets the same number of beads? (Lesson 1C) 18. Working separately, 5 carpenters can make 10 chairs in 2 days. How many chairs can 10 carpenters make in 4 days? (Lesson 1D) Divide. (Lesson 1C) A movie theater has 576 seats arranged in 36 equal rows. How many seats are in each row? 19. Marcy and her friend working separately can make 8 greeting cards in 32 minutes. How many greeting cards can Marcy and her friend make in 48 minutes? (Lesson 1D) 20. E WRITE MATH Suppose you estimate as = 30. Would your estimate be larger or smaller than the exact answer? Explain. (Lesson 1A) 172 Mid-Chapter Check

16 Lowest Number Wins! Divide by Two-Digit Divisors Get Ready! Players: 2, 3, or 4 players Get Set! Each player makes a game sheet like the one shown at the right. You will need: number cubes, index cards Game Sheet Go! Each player rolls a number cube and writes the number rolled in one of the blanks on his or her game sheet. All players find their quotients. The player with the least quotient earns one point. In case of a tie, those players each earn one point. The first person to earn 5 points wins. Game Time Lowest Number Wins! 173

17 Multi-Part Lesson 2 PART Divide Greater Numbers A B C Main Idea I will adjust the quotient when the estimated digit is too high or too low. Adjust Quotients When you estimate which digit to place in the quotient, your estimate might be too small or too large. So, you need to adjust the quotient. Get ConnectED GLE Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI Select a reasonable solution to a realworld division problem in which the remainder must be considered. SPI Solve problems involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE BD- MP3 Player Galina s mother bought her a new MP3 player. The total cost of the MP3 player was $144. The store allowed her to make monthly payments of $16. How many payments will she need to make? Find Step 1 Estimate by using compatible numbers. Step 2 Try the estimate = Since 32 > 16, the estimated digit is too low. Step 3 Adjust. Try 8. Step 4 Adjust again. Try Since 16 = 16, the estimated digit is too low = 9 Check for Reasonableness The estimate, 7, is less than the actual quotient because the dividend was rounded down to 140. So, Galina s mother will need to make 9 payments. 174 Divide by a Two-Digit Divisor

18 It may take several tries to find the best estimate for dividing by a two-digit number. SPORTS CARDS Neil wants to sell his sports cards. He has collected 1,252 sports cards over the past several years. If he sells his cards in packs of 32, how many packs will he be able to sell? Find 1, Step 1 Estimate by using compatible numbers. 1, Division with a Remainder Step 2 Try the estimate , Since 128 > 125, the estimated digit is too high. 1, = 40 Step 3 Adjust. Try 3. Step 4 Bring down the 2 ones. Divide. Try , , = 39 R4 29 < 32 Continue dividing. Check for Reasonableness 39 R4 40 Neil can sell 39 packs with 4 cards remaining , R4 4 < 32 Divide. Check each answer. See Examples 1 and , , , , A crew went net fishing to catch shrimp. They caught 486 shrimp in 54 minutes. How many shrimp did they catch per minute? 10. E TALK MATH Explain how you know when a digit you try in the quotient is too small. Lesson 2A Divide Greater Numbers 175

19 Divide. id Check each answer. See Examples 1 and , , , , , , Brianna made 26 bracelets to sell for a fundraiser. She used a total of 208 beads to make the bracelets. How many beads did she use for each bracelet, if each bracelet has an equal amount of beads? PRACTICE EXTRA Begins on page EP2. Geography Alaska has the longest coastline in the United States. 24. Traveling at 60 miles per hour, how many hours would it take to travel along the Pacific Coast? 25. Alaska has about 31,383 miles of shoreline. A boat travels 33 miles per hour. How long will it take the boat to travel the length of the shoreline? Alaska Coastline Coast Pacific Arctic Miles 5,580 1,060 Alaska Alaska 26. CHALLENGE Find 56,212 divided by FIND THE ERROR Emma estimated the first digit in the quotient of 2, as 4. She adjusted the quotient to 3. What did she do wrong? Explain , > 42 I ll try E WRITE MATH Explain what it means to adjust a quotient. 176 Divide by a Two-Digit Divisor

20 Test Practice 29. Antonio chooses cell phone plan A. It costs him $25 a month. How many minutes does he get per dollar? Monthly Cell Phone Plans Plan Minutes A 450 B 700 A. 21 minutes per dollar B. 16 minutes per dollar C. 25 minutes per dollar D. 18 minutes per dollar 30. Tyree printed 144 pictures from his vacation. He is going to make 12 photo albums to give to his friends. Which is the best estimate for the number of pictures that will be in each album? F. less than 5 G. between 5 and 9 H. between 10 and 20 I. more than SHORT RESPONSE Sheila played a total of 680 minutes for the entire soccer season. If she played an equal amount of time for 20 games, how many minutes did she play each game? Solve. Use the solve a simpler problem strategy. (Lesson 1D) 32. Sixty people can receive a slice of pizza if 5 pizzas are purchased. How many people can receive a slice of pizza if 7 pizzas are purchased? Divide. (Lesson 1C) Estimate. (Lesson 1A) A football team scored 384 points for the season. If there were 16 games, about how many points were scored in each game? (Lesson 1A) 42. James wants to buy a new bike that costs $239. If he wants to save the same amount each month for a year, about how much should he save each month? (Lesson 1A) Lesson 2A Divide Greater Numbers 177

21 Multi-Part Lesson 2 PART Divide Greater Numbers A B C Main Idea I will divide greater numbers by multi-digit divisors. Get ConnectED GLE Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI Solve problems involving the division of twoand three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE , GLE Divide Greater Numbers You can use the standard algorithm or a calculator to divide greater numbers. BD- CONCERTS At a recent rock concert, $22,500 was made from front row ticket sales. If the cost of a single front row ticket was $75, how many people purchased front row tickets? Find 22, Estimate 21, = 300 Step 1 Place the first digit , Step 2 Divide the tens , Step 3 Divide the ones , < < < 75 So, 300 people purchased front row tickets. Check for Reasonableness 300 = Divide by a Two-Digit Divisor

22 To round to the nearest whole number, look at the digit in the tenths place rounds to 306. Determine Reasonable Answers PHONE BOOKS A city phone book has 46,534 names and 152 pages. If each page has about the same number of names per page, how many names are on each page? Sean divided 46,534 by 152. He got 36 for the quotient. Is the quotient reasonable? Step 1 Estimate. 46, , = and 15 are compatible. Since the estimate is 300, Sean s quotient is NOT reasonable. Step 2 Find the quotient using a calculator. Type the following into your calculator Enter The answer in your display screen is So, there would be about 306 names on each page. Estimate. Then divide. Check for reasonableness. See Examples 1 and , , , Turtles and tortoises have long life spans. A tortoise can live for 54,750 days. How many years can a tortoise live? Estimate. Then divide using a calculator. If needed, round the quotient to the nearest whole number , , , E TALK MATH Explain how estimation is used before, during, and after dividing greater numbers. Lesson 2B Divide Greater Numbers 179

23 Estimate. Then divide. id Check for reasonableness. See Examples 1 and , , , PRACTICE EXTRA Begins on page EP , , , There are 14,224 people inside a 56-story building. If the same number of people are on each floor, how many people are on the first floor? Estimate. Then divide using a calculator. If needed, round the quotient to the nearest whole number , , , , , , An average person speaks 35,000 words in one week. Does the average person speak more or less than 2,500 words per day? 23. BAR DIAGRAM If you pay for the golf clubs shown in 24 equal payments, how much will you be paying each month? $2,472 In the first 26 weeks of life, a calf gains about 320 pounds. In the second 26 weeks, it gains about 370 pounds. About how many pounds does a calf gain each week for each of the following? Round to the nearest pound. 24. during the first 26 weeks 25. during the second 26 weeks 180 Divide by a Two-Digit Divisor

24 26. OPEN ENDED Write a division problem that has an estimated quotient of CHALLENGE The dividend below is missing a number. Place a number into the dividend to make the division problem true R , E WRITE MATH Is there a limit to the size of the dividend that can be divided using the strategy learned in this lesson? Explain. Test Practice 29. SHORT RESPONSE Cale solved as shown. Explain the mistake that Cale made and then determine the correct answer. 34 R Lena s mom is having an addition built on their house for $15,650. She has already paid $1,550. She plans to pay the remaining amount in 25 equal payments. How much is one payment? A. $500 B. $564 C. $592 D. $14,100 Solve. Use multiplication to check your answer. (Lesson 2A) , Simon and his family drove 825 miles. They traveled at 55 miles per hour. How much time did it take them? (Lesson 2A) Estimate. Show your work. (Lesson 1A) Lesson 2B Divide Greater Numbers 181

25 Multi-Part Lesson PART 2 Divide Greater Numbers A B C Problem-Solving Investigation Main Idea I will choose the best strategy to solve a problem. ANNIE had 78 inches of plastic string to make keychains. She used 12 inches for one keychain. How many more keychains will Annie be able to make if each keychain is the same size? Understand Plan What facts do you know? The roll of string is 78 inches long. Each keychain is 12 inches long. She has already used 12 inches of string. What do you need to find? How many more keychains Annie will be able to make. Use the guess, check, and revise strategy. Solve Find how much string is left after Annie makes 1 keychain. 78 inches - 12 inches 66 inches There are 66 inches of string left. Use multiplication to find how many 12-inch keychains Annie can make. Guess Check Revise > She can make 5 more keychains with 6 inches of string left over. Check Is the answer reasonable? = 5 R6. GLE Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution. GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. 182 Divide by a Two-Digit Divisor

26 EXTRA % )# E # T4 IC!C 2A 0R P Begins on page EP2. Guess, check, and revise. Solve a simpler problem. Use the four-step plan. Use any strategy shown above to solve each problem. 1. An aquarium at a pet store has 18 Black Neon Tetra fish in it. A customer buys 12 Black Neon Tetra fish at the same time the store clerk adds 7 more Black Neon Tetra fish to the tank. How many Black Neon Tetra fish are in the aquarium now? 2. A fifth grader takes the change from her pocket and places it on the table. The number of each coin she had in her pocket is shown below. Coin Number Quarter 2 Dime 4 Nickel 3 Penny 5 How many different combinations of coins can she make with the coins she has to have $0.45? 5. During the summer Ajay wants to read the books shown. If it takes him 88 days to read all of the books, and each book takes him the same amount of time, how long will it take him to read 1 book? 6. Mr. Reyes baked 4 batches of muffins for his class. Each batch had 12 muffins. If Mr. Reyes has 24 students, how many muffins will each student receive? 7. Measurement Niko has a roll of wrapping paper that had 40 inches on it. He has already used 4 inches for one gift. Does he have enough paper to wrap three gifts that require 12 inches of paper each? Explain. 8. At the soccer banquet everyone was given the choice of chicken, beef, or lasagna for dinner. If 212 people attended the banquet, how many people ordered lasagna? 3. The quotient of two numbers is 20. Their sum is 84. What are the two numbers? Food Number of People Chicken 55 Beef 110 Lasagna 4. Shelli sold 9 tickets for the school play and collected $78. Upper-level tickets cost $6. Ground-level tickets cost $10. How many of each kind of ticket was sold? 9. E WRITE MATH Refer to Exercise 3. Explain how you used the guess, check, and revise strategy to find the numbers. To assess mastery of SPI , see your Tennessee Assessment Book. 183

27 Did you know you have between 206 and 300 bones in your body? A healthy diet makes them strong strong, and calcium is an important part of a healthy diet. Adults need only 1,000 milligrams of calcium each Your bones grow until you are 30 years old. 184 Divide by a Two-Digit Divisor day, but fifth graders should eat or drink about 1,200 milligrams. The calcium you eat or drink is deposited in your bones. Therefore, your bones are a bank for calcium!

28 Use the information on the previous page to solve each problem. 1 If you eat 1 ounce of cheddar cheese, how much calcium willl you deposit in your bone bank? Solve lve mentally. ou u have cups cu ups of of ice ic cream in 5 YYou 2 weeks. w ek we ks. s How How much muc m uch h calcium calc ca lciu i m will you u consume co ons nsum ume in each eac e acch cup? cup? 2 Suppose you eat twelve cups of yogurt in one week. How much h calcium will you eat in one day? y? nd a 3 Toni had a cup of skim milk and cup of yogurt for breakfast. How w much calcium was in Toni s breakfast? ld 4 How much more calcium would a cup of carrots and a cup of yogurt have than a cup of skim milk? Problem Solving in Health 185

29 Chapter Study Guide and Review Be sure the following Key Concepts are noted in your Foldable. Vocabulary compatible numbers dividend Estimate Quotients with Two-Digit Divisiors Divide by a Two-Digit Divisor divisor quotient Adjust Quotients Divide Greater Numbers remainder rounding Key Concepts Estimate Quotients with Two-Digit Divisors (Lesson 1) Find compatible numbers for 315 and Divide by Two-Digit Divisors (Lesson 1) Adjust Quotients (Lesson 2) Estimate = and 60 are compatible because 30 6 = 5. Bring down the ones = = = 0 Since 288 > 251, the estimated digit is too high. Adjust. Try 5. 5 R Vocabulary Check State whether each sentence is true or false. If false, replace the underlined word or number to make a true sentence. 1. The answer to a division problem is 534 R4. The R stands for reduce. 2. In the division sentence = 50, 50 is the dividend. 3. Compatible numbers are numbers that are easy to divide mentally = In the division sentence = 28, 22 is the divisor. 186 Divide by a Two-Digit Divisor

30 Multi-Part Lesson Review Lesson 1 Divide by Two-Digit Divisors Estimate Quotients with Two-Digit Divisors (Lesson 1A) Estimate each quotient. Show your work Tito purchased 11 tickets to a baseball game for $374. About how much did one ticket cost? EXAMPLE 1 Estimate Round the divisor to the nearest ten = 7 Change the dividend to a number that is compatible with 5. So, is about 7. Divide by Two-Digit Divisors (Lesson 1C) Divide Tonya saved $564 in one year. If she saved the same amount each month, how much did Tonya save in one month? EXAMPLE 2 Find So, = 11. Problem-Solving Strategy: Solve a Simpler Problem (Lesson 1D) Solve. Use the solve a simpler problem strategy. 16. Bennett is placing photographs in an album. He will put the same number of photos on each of the 13 pages. If he can put 4 pictures in a row, how many rows will be on each page? EXAMPLE 3 A school rents 5 buses to take 215 students on a field trip. If each bus can take the same number of students, how many students will be on two buses? Step 1 Find how many students fit on one bus = 43 Step 2 Multiply 43 by 2 to find the number of students on 2 buses = 86 So, 86 students can fit on 2 buses. Chapter Study Guide and Review 187

31 Chapter Study Guide and Review Lesson 2 Divide Greater Numbers Adjust Quotients (Lesson 2A) Divide. Check each answer , , A jet ski costs $3,204. If you want to make 36 equal payments, how much is one payment? EXAMPLE 4 Find Estimate = 5 Try the estimate. 5 Since 83 = 83, the estimated digit is too low. 83 Adjust. Try 6. So, = Divide Greater Numbers (Lesson 2B) Estimate. Then divide. Check for reasonableness , ,400 Estimate. Then divide using a calculator. If needed, round the quotient to the nearest whole number , ,658 EXAMPLE 5 Find 25, ,600 Estimate 30, = So, 25, = 400. Problem-Solving Investigation: Choose the Best Strategy (Lesson 2C) Choose the best strategy to solve the problem. 26. Sandra has 4 shirts and 3 pants. If she wears a different combination of shirt and pants each day, how many days until she repeats an outfit? 27. How many ways are there to represent $0.77 using at least two quarters and only two pennies? EXAMPLE 6 Andre is using a rectangle, a triangle, and a circle to create a pattern. How many different ways can he arrange the shapes to form a repeating pattern if he uses each shape once? There are 6 ways to arrange the shapes. 188 Divide by a Two-Digit Divisor

32 Practice Chapter Test Estimate each quotient. Show your work John bought 11 packages of tennis balls for $132. About how much did one package cost? 6. MULTIPLE CHOICE The table shows the number of deer in a wildlife preserve and the size of the preserve in acres. Which is the best estimate for the number of deer per acre? Number of Deer 406 Number of Acres 38 A. 1 C. 100 B. 10 D. 1, MULTIPLE CHOICE Dario sold three times as many wristbands as headbands. If he sold 10 headbands, how much money did he earn in all? Divide. Item Cost Headbands $6 T-shirts $12 Wristbands $6 F. $60 H. $240 G. $180 I. 1, , , , ,652 Divide Trevon is making payments on a computer that costs $1,548. If he makes 12 equal payments, how much is one of his payments? Estimate. Then divide using a calculator. If needed, round the quotient to the nearest whole number , , , , Jillian read 336 pages in 42 days. If she read the same amount each day, how many pages did she read in one day? 24. E WRITE MATH Write a real-world division problem that can be solved using the act it out strategy. Practice Chapter Test 189

33 Test Practice Ms. Flores drove 360 miles. If she drove 45 miles each hour, how many hours did she drive? A. 5 C. 7 B. 6 D. 8 You can estimate using compatible numbers or rounding to check the reasonableness of answers. Read the Test Item You need to divide the number of miles by the speed she traveled to find how many hours she drove. Solve the Test Item Divide 360 by 45 to find the number of hours she drove The answer is D. Check 45 8 = 360 Read each question. Then fill in the correct answer on the answer sheet provided by your teacher or on a separate sheet of paper. 1. It costs $54 to purchase 6 movie tickets. How much does it cost for 1 movie ticket? 2. The coach purchased 13 jerseys for the basketball team for $312. Which expression can be used to find the cost of each jersey? F. 13 $312 G. $ A. $5 C. $8 B. $6 D. $9 H. $ I. 13 $ Divide by a Two-Digit Divisor

34 3. Find the quotient of the division expression shown below A. 3 C. 75 B. 30 D SHORT RESPONSE It takes Javier 720 seconds to run two miles. Explain how to find the number of minutes it takes Javier to run two miles. 5. GRIDDED RESPONSE Lacey s dad bought the GPS system shown for his car. He made 3 equal payments. What was the amount of each payment in dollars? $ GRIDDED RESPONSE The principal has 322 certificates to give to 14 teachers. Each teacher receives the same number of certificates. How many certificates will 2 teachers receive combined? 8. Brandy is purchasing prizes for her party games. She spent $18 on stickers and bracelets. How many of each prize did she purchase? Prize Cost stickers 3 for $5 bracelets 2 for $4 A. 9 stickers and 2 bracelets B. 6 stickers and 6 bracelets C. 6 stickers and 4 bracelets D. 9 stickers and 4 bracelets 9. Carlos looks at his car s odometer shown below to see the total distance his car has traveled in 9 years. About how many miles has the car traveled each year? 6. Erika sent 384 text messages in one year. If she sent the same number of messages each month, how many messages did she send in December? F. 32 H. 45 G. 40 I. 50 F. less than 9,000 miles G. between 9,000 and 15,000 miles H. between 15,000 and 20,000 miles I. greater than 20,000 miles NEED EXTRA HELP? If You Missed Question Go to Chapter-Lesson A 4-1C 4-1A 4-1A 3-2D 4-1A 4-1D 3-1E 4-1A For help with... SPI 2.4 SPI 2.4 GLE 2.3 GLE 2.3 SPI 2.4 GLE 2.3 GLE 1.2 GLE 1.2 GLE 1.2 Test Practice 191